{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Variational Equations\n",
    "For a complete introduction to variational equations, please read the paper by Rein and Tamayo (2016).\n",
    "\n",
    "For this tutorial, we work with a two planet system. We vary the initial semi-major axis $a$ of the outer planet. Because the planets interact with each other, the final $x$-position of the inner planet at the end of the simulation will depend on the initial semi-major axis of the outer planet. We run the simulation once for a fixed $a_0$ and then use first and second order variational equations to predict the final position of the outer planet for different $a$s in a neighbourhood of $a_0$. \n",
    "\n",
    "To do that, let us first import REBOUND, numpy and matplotlib."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "scrolled": false
   },
   "outputs": [],
   "source": [
    "import rebound\n",
    "import numpy as np\n",
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "from matplotlib.ticker import FormatStrFormatter"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Before using variational equations, let us define a function that calculates the final position of the inner planet as a function of $a$ in the brute-force way:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def run_sim(a):\n",
    "    sim = rebound.Simulation()\n",
    "    sim.add(m=1.)\n",
    "    sim.add(primary=sim.particles[0],m=1e-3, a=1)\n",
    "    sim.add(primary=sim.particles[0],m=1e-3, a=a)\n",
    "    \n",
    "    sim.integrate(2.*np.pi*10.)\n",
    "    return sim.particles[1].x"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We'll use this function to create a list of *true* final positions to which we later compare our results."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "N=400\n",
    "x_exact = np.zeros((N))\n",
    "a_grid = np.linspace(1.4,1.7,N)\n",
    "for i,a in enumerate(a_grid):\n",
    "    x_exact[i] = run_sim(a)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Running a simulation with variational equations is very easy. We start by creating a simulation and add the three particles (the star and two planets) just as before. Note that the `vary` convenience function we use below only accepts heliocentric coordinates, so we explicitly tell REBOUND that the star is the primary when adding particles to the simulation. \n",
    "\n",
    "We then add variational particles to the simulation. We vary one parameter ($a$) and thus need only one set of first order variational equations. The second order variational equations depend on the first order ones. Thus, when initializing them, one has to pass the set of first order variational equations using the 'first_order' parameter.\n",
    "\n",
    "After adding a variation, one must always initialize it.  We do this below with REBOUND's `vary()` convenience function, which makes varying orbital parameters particularly easy. Alternatively, one can also initialize the variational particles directly, e.g. using  `var_da.particles[1].x = 1`. Note that variations are implemented as particles, but you they really represent derivatives of a particle's coordinates with respect to some initial parameter. For more details, see Rein and Tamayo (2016).\n",
    "\n",
    "The function below does all that and returns the final position of the inner planet, as well as the first and second derivatives of the position with respect to $a$. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def run_sim_var(a):\n",
    "    sim = rebound.Simulation()\n",
    "    sim.add(m=1.)\n",
    "    sim.add(primary=sim.particles[0],m=1e-3, a=1)\n",
    "    sim.add(primary=sim.particles[0],m=1e-3, a=a)\n",
    "    var_da = sim.add_variation()\n",
    "    var_dda = sim.add_variation(order=2, first_order=var_da)\n",
    "    var_da.vary(2, \"a\")\n",
    "    var_dda.vary(2, \"a\")\n",
    "    \n",
    "    sim.integrate(2.*np.pi*10.)\n",
    "    return sim.particles[1].x, var_da.particles[1].x, var_dda.particles[1].x"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can now use the variational equations to predict the final position of the inner particle. Note that we only run one simulation, at $a_0=1.56$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "a_0 = 1.56\n",
    "x, dxda, ddxdda = run_sim_var(a_0)\n",
    "x_1st_order = np.zeros(N)\n",
    "x_2nd_order = np.zeros(N)\n",
    "for i,a in enumerate(a_grid):\n",
    "    x_1st_order[i] = x + (a-a_0)*dxda\n",
    "    x_2nd_order[i] = x + (a-a_0)*dxda + 0.5*(a-a_0)*(a-a_0)*ddxdda"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the figure below, we plot the final position as a function of the initial semi-major axis. The black line corresponds to the true final position as calculated by the brute-force approach. The dashed and dotted lines correspond to the approximations using first and second order variational equations. As one can see, the second order approximation is very accurate within a neighbourhood of $a_0$. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 600x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(6,4))\n",
    "ax = plt.subplot(111)\n",
    "ax.set_xlim(a_grid[0],a_grid[-1])\n",
    "ax.set_ylim(np.min(x_exact),np.max(x_exact)*1.01)\n",
    "ax.set_xlabel(\"initial semi-major axis of the outer planet\")\n",
    "ax.set_ylabel(\"$x$ position of inner planet after 10 orbits\")\n",
    "ax.plot(a_grid, x_exact, \"-\", color=\"black\", lw=2)\n",
    "ax.plot(a_grid, x_1st_order, \"--\", color=\"green\")\n",
    "ax.plot(a_grid, x_2nd_order, \":\", color=\"blue\")\n",
    "ax.plot(a_0, x, \"ro\",ms=10);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "For chaotic systems, the coordinates of variational particles grow exponentially. Very quickly, one might run into numerical issues because the finite range of floating point numbers prevents us from working with number larger than $\\approx10^{308}$. REBOUND (as of version 3.21) automatically rescales first order variational variables when coordinates become larger than $10^{100}$. This is possible because first order variational equations (in contrast to second order ones) are linear.\n",
    "\n",
    "Consider the following chaotic planetary system:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "sim = rebound.Simulation()\n",
    "sim.add(m=1.) # Star\n",
    "sim.add(m=0.000954, a=5.204, M=0.600, omega=0.257, e=0.048) # planet 1\n",
    "sim.add(m=0.000285, a=7.2, M=0.871, omega=1.616, e=0.12)    # planet 2\n",
    "sim.move_to_com()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let us add a first order set of variational equations:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "v = sim.add_variation()\n",
    "v.particles[1].x = 1 "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next, we integrate this forward in time, keeping track of the x coordinate of the variational particle as well as the `lrescale` parameter in the `reb_variational_configuration` struct `v`. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "sim.integrator = \"whfast\"\n",
    "sim.dt = 5.0\n",
    "times = np.linspace(0,1e6,1000)\n",
    "xs = np.zeros(len(times))\n",
    "lrescale = np.zeros(len(times))\n",
    "\n",
    "for i in range(len(times)):\n",
    "    sim.integrate(times[i], exact_finish_time=0)\n",
    "    xs[i] = v.particles[1].x\n",
    "    lrescale[i] = v.lrescale"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can then use `lrescale` to extend our integration beyond what would normally be possible using standard floating point numbers. The `lrescale` parameter is the logarithm of all rescalings that have been applied to the variational particles. Note that we need to do all the calculations in log space because the values are too big for floating point numbers."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "log_xs = np.log(np.abs(xs)) + lrescale\n",
    "log10_xs = log_xs/np.log(10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()\n",
    "ax.set_ylabel(\"$|x|$\")\n",
    "ax.set_xlabel(\"time [orbits]\")\n",
    "ax.plot(times/sim.particles[1].P, np.log10(np.abs(xs)), label= \"actual x coordinate of variational particle \\n (not taking rescaling into account)\")\n",
    "ax.plot(times/sim.particles[1].P, log10_xs, label= \"x coordinate of variational particle \\n (rescaling taken into account)\")\n",
    "plt.axhline(y=308, color='k', linestyle='--', label = \"maximum range of floating point numbers\")\n",
    "ax.yaxis.set_major_formatter(FormatStrFormatter('$10^{%.f}$'))\n",
    "ax.legend(loc=\"upper left\");"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}
